login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A253249 Number of nonempty chains in the divides relation on the divisors of n. 72
1, 3, 3, 7, 3, 11, 3, 15, 7, 11, 3, 31, 3, 11, 11, 31, 3, 31, 3, 31, 11, 11, 3, 79, 7, 11, 15, 31, 3, 51, 3, 63, 11, 11, 11, 103, 3, 11, 11, 79, 3, 51, 3, 31, 31, 11, 3, 191, 7, 31, 11, 31, 3, 79, 11, 79, 11, 11, 3, 175, 3, 11, 31, 127, 11, 51, 3, 31, 11, 51 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For prime p, a(p)=3.

a(2^k) = 2^(k+1)-1.

For integers of the form n = p_1*p_2*...*p_k we have a(n) = A007047(k).

The value of a(n) depends only on the exponents in the prime factorization of n.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..20000

FORMULA

Dirichlet g.f.: zeta(s)^2*A(s) where A(s) is the Dirichlet g.f. for A074206. - Geoffrey Critzer, May 23 2018

Sum_{k=1..n} a(k) ~ -4*n^r / (r*Zeta'(r)), where r = A107311 = 1.728647238998183618135103... is the root of the equation zeta(r) = 2. - Vaclav Kotesovec, Jan 31 2019

a(n) = 4*A002033(n-1) - 1 for n > 1. - Geoffrey Critzer, Aug 19 2020

EXAMPLE

a(10) = 11 because we have: {1}, {2}, {5}, {10}, {1|2}, {1|5}, {1|10}, {2|10}, {5|10}, {1|2|10}, {1|5|10}.

MAPLE

with(numtheory):

b:= proc(n) option remember: 1+ `if`(n=1, 0,

       add(b(d), d=divisors(n) minus {n}))

    end:

a:= n-> add(b(d), d=divisors(n)):

seq(a(n), n=1..100);  # Alois P. Heinz, Jun 04 2015

MATHEMATICA

Table[Total[Table[Length[Select[Subsets[Divisors[n], {k}], Apply[And, Map[Apply[Divisible, #] &, Partition[Reverse[#], 2, 1]]] &]], {k, 1, PrimeOmega[n] + 1}]], {n, 1, 100}]

CROSSREFS

Cf. A002033, A007047, A074206, A107311.

Sequence in context: A135434 A204204 A164928 * A069949 A143275 A083262

Adjacent sequences:  A253246 A253247 A253248 * A253250 A253251 A253252

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jun 04 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 18:55 EDT 2022. Contains 356949 sequences. (Running on oeis4.)